Electric field direction and permittivity

[zrek]

The electric field direction can be measured by the force affected on a test charge.

Let's put a point-like charge not far from a material, that is polarized by it.
See the figure:

The test force on the test charge A points exactly to the charge.

I think that because the surface is full of polarized particles in one direction, the test charge next to the surface (C) will behave differently, the force on it will points more perpendicular to the surface.

And also the inner test charges (like B) will be under the effect of the neighbour particles, so the direction of the force will point a little towards the surface.

Is this effect possible? Can the permittivity affect to the direction of the force?

Thank you for your toughts.

 

[mfb]

The test force on the test charge A points exactly to the charge.

There should be a slight deviation due to the material below it.

Is this effect possible? Can the permittivity affect to the direction of the force?

Yes it can.

 

[zrek]

Yes it can.

Is it calculatable somehow? For example like the Snell's law?

 

[mfb]

With the boundary conditions for electromagnetic fields - the parallel component of E and the perpendicular component of D are continuous, the field inside the material and outside are divergence-free, and D and E are proportional to each other* with some material constants.

For the surface, this should give something similar to Snell's law I think.

*there are materials where this is not true. It does not change the basic concept, however.

 

[zrek]

... the field inside the material and outside are divergence-free...

Am I understand it well that inside the material the force on the test charge points (in avarage) exactly to the main point-charge?

 

[mfb]

No, the direction there will be changed by the material, too.

 

[zrek]

I googled the net, but I have not found relevant information about this. Please if anyone have a link about the calculation of how the force direction change inside the material, share this info, I'd be happy.
Thank you in advance!